document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=566162>Question 566162</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The question is: what is the sum of 4+11+18+....+4001<BR>\n" );
document.write( "I have been taught to add the first and last number, so i get 4005. Then I usually divide by half of the last number, which would be 2000.5<BR>\n" );
document.write( "However, I know this only works if the numbers go up by one, not seven. This is where I get lost. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #366160 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=366160\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let S = the sum you want. Then, we have\r<BR>\n" );
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document.write( "S = 4  +  11+18+...+4001<BR>\n" );
document.write( "S = 4001+3994 + ... + 4\r<BR>\n" );
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document.write( "If we add them up, we get 2S = 4005 + 4005 + ... + 4005. Now we have to count the number of \"4005s\" there are, which is equal to the size of the set {4, 11, 18, ..., 4001}. This is equal to the size of the sets {7, 14, 21, ..., 4004} and {1, 2, 3, ..., 572} (we are just adding or multiplying numbers in the sets by a fixed number; this does not change the size of the set).\r<BR>\n" );
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document.write( "Therefore, there are 572 \"4005s.\" Hence, 2S = 572*4005, S = 572*4005/2 = 1145430. </SPAN>\n" );
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